Remark 4.2 
If \(\sigma _2=f_1=f_2=b_2=\sigma _3=f_3\equiv 0\) , \(g\)  is independent of \(z^2,\tilde{z}^1,\tilde{z}^2\)  with \(z^2=\tilde{z}^1=\tilde{z}^2=0\) , then Theorem REF  reduces to Theorem 2 of Hu [1]}. Furthermore, when the control domain is convex, Theorem REF  can reduce to Theorem 4.4 of Peng [2]} in which “\(l=h\equiv 0\) ". Moreover, if we reset \(\tilde{p}=p,\tilde{q}=q\)  which satisfies
\(\left\lbrace \begin{aligned}-d\tilde{p}(t)&=\big [(g_y+g_z\sigma _x+f_x)\tilde{p}+(g_z+\sigma _x)\tilde{q}+g_x\big ]dt-\tilde{q}dW_t,\quad t\in [0,T],\\\tilde{p}(T)&=0.\end{aligned}\right.\) 
